Incremental Encoder Position Interpolation

ABSTRACT

An interpolated position of an incremental encoder is provided. A first signal and a second signal having a quadrature relationship are received from the incremental encoder. A coarse position of the incremental encoder at a first time is produced using the quadrature relationship between the first signal and the second signal. An arcsine or arccosine value based on the first signal at the first time is determined using a lookup table and a fine position of the incremental encoder is calculated using the determined value. The interpolated position of the incremental encoder, based on both the coarse position and the fine position, is then provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/515,990 (now U.S. Pat. No. 11,XXX,XXX) entitled Incremental EncoderPosition Interpolation and filed on Jul. 18, 2019, which is herebyincorporated by reference in its entirety herein for any and allpurposes.

BACKGROUND Technical Field

The present subject matter relates to position encoders, and morespecifically, to an interface for an incremental position encoder thatinterpolates quadrature signals to calculate a more accurate position ofthe incremental encoder.

Background Art

Position encoders that provide one or more signals to indicate movementof a tracked element of the encoder are well known in the art. Aposition encoder may be used to track rotation of a shaft or otherobject and may be referred to as a rotary encoder. Other embodiments ofan encoder may be used to track linear motion of a component and may bereferred to as a linear encoder. An incremental encoder does not providean absolute position of the tracked element as it moves, but providesone or more signals to indicate of movement of the element. An absoluteencoder provides information about the current position of the trackedelement of the encoder, such as a shaft of an absolute rotary encoder.

Many incremental encoders have two outputs that provide signals with a90° phase relationship (i.e. a quadrature relationship) to each other asthe tracked element moves. These signals may be used to determine both adirection of movement and an amount of movement of the tracked element.The frequency of the signals is proportional to a velocity of thetracked element and the phase difference between the two signals can beused to determine the direction of movement.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute partof the specification, illustrate various embodiments. Together with thegeneral description, the drawings serve to explain various principles.In the drawings:

FIG. 1 is a block diagram of a system with a rotary incremental encoderand an embodiment of an apparatus to provide an interpolated position ofthe incremental encoder;

FIG. 2A shows an example of a rotary encoding disc of a rotaryincremental encoder;

FIG. 2B shows detail of a section of the rotary encoding disc of FIG.2A;

FIG. 3A shows various waveforms and generated values of an embodiment;

FIG. 3B shows a state diagram for an embodiment of a quadrature-trackingstate machine;

FIG. 4 is a block diagram of an embodiment of an apparatus to provide aninterpolated position of an incremental encoder; and

FIG. 5A-5G are flowcharts showing various aspects of an embodiment of amethod to provide an interpolated position of an incremental encoder.

DETAILED DESCRIPTION

In the following detailed description, numerous specific details are setforth by way of examples in order to provide a thorough understanding ofthe relevant teachings. However, it should be apparent to those skilledin the art that the present teachings may be practiced without suchdetails. In other instances, well known methods, procedures andcomponents have been described at a relatively high-level, withoutdetail, in order to avoid unnecessarily obscuring aspects of the presentconcepts. A number of descriptive terms and phrases are used indescribing the various embodiments of this disclosure. These descriptiveterms and phrases are used to convey a generally agreed upon meaning tothose skilled in the art unless a different definition is given in thisspecification.

Incremental encoders are used in many different applications. Anincremental encoder can measure linear movement or rotational movement.While the concepts described herein are, in general, applicable to bothlinear and rotary encoders, most of the embodiments discussed herein arerotary encoders. Nonetheless, use of the concepts described herein forlinear encoders is envisioned. Any type of encoder technology may beused for the incremental encoder, including mechanical contact ofconductors, optical technology, magnetic technology, or capacitivetechnology, as non-limiting examples. That being said, an opticalencoder is used for the examples herein.

An optical encoder may include a rotating disc with two concentric ringsof alternating transparent and opaque areas. A second opaque elementincludes a slit or other opening that is positioned adjacent to the discso that as the disc rotates, light from a light source on one side ofthe rotating disc can only shine through at most one transparent area ofeach of the two concentric rings of the disc at a time. A light sensormay be positioned on the other side of the disc/slit combination foreach of the two concentric rings to detect light passing through thetransparent areas of each of the rings. The outputs of the light sensorsmay be used to generate quadrature-encoded analog signal outputs for theencoder that may essentially be a sine wave and a cosine wave generatedat a common frequency based on the speed of rotation of the disc.

An apparatus may receive the quadrature-encoded analog signals from theencoder and determine an interpolated position of the encoder (i.e. aninterpolated position of the encoding disc in the encoder). Theapparatus may be known by a variety of different names including anencoder interface or an encoder controller as non-limiting examples. Theinterpolated position may be determined by calculating a coarse positionand a fine position which is added to the coarse position. The coarseposition may have a resolution equivalent to between one cycle of thequadrature-encoded signals and one quarter of a cycle of the signals.The fine position provides an interpolation of the coarse positionresolution. The interpolated position may be determined as a number ofdegrees, a number of rotations, a number of cycles of the signals, orany other unit, depending on the embodiment, and may include a wholenumber part and a fractional part in some embodiments. The interpolatedposition may be positive or negative in some embodiments to represent amovement from an index, or home, position. In at least one embodimentthe interpolated position is calculated based on a unit equal to onequarter of the amount of rotation required to generate a full cycle ofthe quadrature-encoded signals, with the coarse position having aresolution of one unit and the fine position having a fractional valueof between 0 and 1. In another embodiment the fine position may becalculated as a whole number between 0 and 999, with the coarse positionincreasing by 1000 for every full cycle of the quadrature-encodedsignals.

In embodiments, the apparatus may generate two digital signals, A and B,based on the two quadrature-encoded analog signals, although in someembodiments, equivalent signals may be provided to the apparatus alongwith the quadrature-encoded analog signals (or data stream representingthe quadrature-encoded signals). The A signal may be set to a ‘1’ if thesine signal is greater than a zero-crossing value and set to a ‘0’ valueis the sine signal is less than the zero-crossing value. The B signalmay be set to a ‘1’ if the cosine signal is greater than itszero-crossing value (which may be the same or different than thezero-crossing value for the sine signal) and set to a ‘0’ value is thecosine signal is less than the zero-crossing value. By determiningwhether the A signal leads B (a positive phase difference), or the Bsignal leads A (a negative phase difference), the direction of rotationcan be determined, and the movement of the encoder determined down toone quarter of the arc per cycle. This may be accomplished through theuse of a simple state machine as shown in FIG. 3B (which can beimplemented as an asynchronous state machine or a synchronous statemachine) and a counter to track the cumulative motion.

So, for example, if each of the analog quadrature-encoded signals have afull cycle generated by one degree of rotation of the disc in theencoder, the A and B signals can be used to track the movement of thedisc to a resolution of 15 minutes of arc (one quarter of 1° or 1quarter of a pulse cycle) by using the quadrature-tracking state machineof FIG. 3B. Various embodiments may use a different state machine thatmay provide a lower resolution of tracking, such as a resolution of onehalf of a pulse cycle or a resolution of one pulse cycle which may allowthe state machine to more reliably control the counter in a high-speedasynchronous embodiment.

The apparatus also uses the phase of the quadrature-encoded signals tocalculate the fine position. In embodiments, the apparatus may digitizetwo analog quadrature-encoded signals and use the digital values tocalculate a tangent value by dividing the value of the sine signal bythe value of the cosine signal and then calculating the arctangent valueto determine the fine position. While dividing the sine by the cosine todetermine a tangent value may help to minimize errors due to asymmetriesand noise in the analog signals, tangent values are unbounded, making itdifficult to use a table lookup to calculate an arctangent value.

In other embodiments, the arcsine of the sine value or the arccosine ofthe cosine value may be calculated to determine the fine position.Because sine and cosine values are both bounded between 1 and −1, atable lookup can be utilized to calculate an arcsine or arccosine value.Asymmetry and/or noise in the sine/cosine signals, however, may lead toerrors in the calculated fine position. Techniques are described hereinfor calibrating the sine/cosine signals to minimize those errors. Notethat while the descriptions herein mostly discuss the calculation of thearcsine value of the sine signal, similar techniques can also be used togenerate an arccosine value of the cosine signal.

A zero-crossing value for the sine signal may be calculated based onsome number of previous local extrema for the sine signal and finding amidpoint between a local maximum and a local minimum of the sine signal.In some embodiments, a maximum and minimum of the sine signal over arange of motion of the encoder may be found and the zero-crossingcalculated as a midpoint between the maximum and minimum of that range,with that zero-crossing value used for both the generation of the A andB digital signals described above and the calculation of the arcsinevalue for the full range of motion of the encoder. A similar operationmay be used on the cosine signal to calculate a zero-crossing value forcosine. In at least one embodiment, the most recent local maximum andlocal minimum are used to calculate a current zero-crossing value thatvaries dynamically for each cycle of the signal as the disc of theencoder moves, but in other embodiments, a predetermined number of localmaxima and local minima are used to calculate a current zero-crossingvalue as a moving average. Varying the zero-crossing value dependentupon the position of the encoder can help compensate for errors in thesine value due to eccentricity of the disc in the encoder, noise, orother errors in the outputs of the encoder.

Another calibration technique may find a local maximum of the sinesignal and then use the value of the cosine signal at that point to seta zero-crossing value for the cosine signal falling and find a localminimum value of the sine signal and then use the value of the cosinesignal at that point to set a zero-crossing value for the cosine signalrising. This may help compensate for phase errors in the cosine signalas compared to the sine signal.

The arcsine (or arccosine) may be calculated using any method, but insome embodiments, a lookup table may be used. The lookup table may storevalues for all four quadrants of the signal, two quadrants, or a singlequadrant, depending on the embodiment. The size of the lookup table maybe based on a number of bits used to represent the signal. For example,if a 12-bit analog-to-digital converter is used, a lookup table with2048 entries could be used for an embodiment storing a single quadrantof values, with 4096 entries and 8192 entries stored, respectively, fortwo quadrant and four quadrant embodiments.

In some embodiments, a scaling factor is used to scale a maximum valueof the signal to the maximum lookup table address to ensure that thefull range of the arcsine values are utilized. The difference betweenthe digitized sine value and the zero-crossing value is multiplied bythe scaling factor and then used as the lookup address. In multiplequadrant embodiments, one or two bits describing the quadrant may alsoused as a part of the lookup address.

The fine position can be determined based on the quadrant as follows:Q0: sin⁻¹(F*(S−Z)); Q1: C−sin⁻¹(F*(S−Z)); Q2: sin⁻¹(F*(Z−S)); and Q3:C−sin⁻¹(F*(Z−S)); where C is the resolution of the coarse position, F isthe scaling factor, Z is the zero-crossing value for the sine signal,and S is the value of the sine signal. If all four quadrants are storedin the lookup table, the full fine position can be directly stored inthe lookup table with the lookup address being F*(S−Z) with one bit morethan the digitized value of S to allow a twos-compliment value begenerated for the Q2 and Q3 and the least significant bit of thequadrant identifier used as another address bit. If Q0 and Q1 are storedin the lookup table, then the least significant bit of the quadrantidentifier may used as an address bit of the lookup table and the mostsignificant bit of the quadrant identifier used to determine whether tocalculate S−Z or Z−S. In some embodiments, the lookup table storesvalues for Q0 and the quadrant identifier is used to determine whetherto use S−Z or Z−S in the address calculation and whether to use thelookup table output directly as the fine position or subtract the lookuptable output from C to calculate the fine position. The fine positioncan then be added to the coarse position to provide an interpolatedposition for the encoder.

Any type of electronic circuitry may be used for the apparatus toprovide an interpolated encoder position, including, but not limited to,a custom application-specific integrated circuit (ASIC), a circuit boardwith one of more active electronic components, and/or a processorrunning software stored in a memory. A field-programmable gate array(FPGA) is used in at least one embodiment. The FPGA may be coupled to amemory storing configuration information for the FPGA which, once loadedinto the FPGA, configure various circuits of the FPGA to provide aninterpolated encoder position as described herein.

Reference now is made in detail to the examples illustrated in theaccompanying drawings and discussed below.

FIG. 1 is a block diagram of a system 100 with a rotary incrementalencoder 140 and an embodiment of an interpolator 160 to provide aninterpolated position of an incremental encoder. The rotary incrementalencoder (or position encoder) 140 may be a linear encoder or a rotaryencoder and the embodiment shown uses optical technology to detectmotion of a carrier 110 (e.g. a disc) which is coupled 192 to astructural member 190 of the system 100 so that the carrier 110 movesbased on motion of the structural member 190. The coupling 192 may useany type of interaction between the structural member 190 and thecarrier 110 including, but not limited to, mounting the carrier 110 on ashaft upon which the structural member 190 rotates, gears and/or beltsdriven by motion of the structural member 190 to drive a shaft or anedge of the carrier 110, and physical attachment of the carrier 110 tothe structural member 190. The coupling 192 may provide a fixedrelationship between motion of the structural member 190 and the carrier110 so that a position of the carrier 110 may be used to describe aposition of the structural member 190.

The system 100 may also include a controller 150, coupled to the encoder140, a computer 180 which is coupled to the controller 150 and may issuecommands to the controller 150 over the command interface 182, and anactuator 170 which can move the structural member 190 and may be undercontrol of the controller 150 through the actuator interface 172. Theactuator 170 may be any type of motor, hydraulic system, pneumaticsystem, or other mechanism capable of moving the structural member 190.

The position encoder 140 includes a light source 102, an opaque element105, the carrier 110, positioned adjacent to the opaque element 105, afirst sensing element 136, and a second sensing element 138 which may belight-sensitive transistors in some embodiments. A first output 146 iscoupled to the first sensing element 136 and a second output 148 iscoupled to the second sensing element 138. The first sensing element 136is positioned to receive light from the light source 102 that may passthrough the hole 126 in the carrier 110 when it is lined up with a slit108 in the opaque element 105 and the second sensing element 138 ispositioned to receive light from the light source 102 that may passthrough the hole 128 in the carrier 110 when it is lined up with a slit108 in the opaque element 105. The encoder 140 is configured to providea first signal at the first output 146 and a second signal at the secondoutput 148 with the first signal having a quadrature relationship withthe second signal. In some embodiments the first signal may be referredto as a sine signal and the second signal may be referred to as a cosinesignal. The position encoder 140 provides incremental motion indicationsusing the first signal and the second signal which are based on motionof the structural member 190 through its coupling 192 with the carrier110.

The controller 150 may be coupled to the position encoder 140 by througha first input 156 and a second input 158. The controller 150 may alsoinclude the actuator interface 172 to control the actuator 170 and thecommand interface 182 to receive commands. The controller 150 may alsoinclude an interpolator 160 for providing an interpolated position ofthe position encoder 140 which may be constructed using electroniccircuitry of any type, including, but not limited to a processor andmemory 162 storing instructions 164 to be executed by the processor, apurpose-designed integrated circuit, a field-programmable gate array(FPGA) with memory 162 storing configuration information 164 for theFPGA, or any other type and arrangement of active and passive electroniccircuitry.

Thus, embodiments may include an article of manufacture comprising anon-transitory storage medium 162 having instructions 164 stored thereonthat, if executed, result in one or more methods being performed. Notethat the instructions 164 may be configuration information for an FPGAin some embodiments and that executing may refer to configuring the FPGAbased on the configuration information to perform one or more methods.

One method that may be performed by the interpolator 160 using theinstructions 164 stored on in the memory 162 includes receiving a firstsignal from an incremental encoder 140 and producing a coarse positionof the incremental encoder 140 based on the first signal. The firstsignal may be received on the first input 156. A lookup value isretrieved from a lookup table based on the first signal and a fineposition of the incremental encoder is calculated using the lookupvalue. An interpolated position of the incremental encoder based on boththe coarse position and the fine position is then provided. In someembodiments, the interpolated position may be provided through thecommand interface 182 to the computer 180.

In some embodiments, the method performed by the apparatus 160 using theinstruction 164 stored in the memory 162 includes obtaining a digitalvalue of the first signal and ascertaining a quadrant of the firstsignal at a first time. A first zero-crossing value is established forthe first signal and a lookup address is computed based on the digitalvalue and the first zero-crossing value. The lookup address is used toretrieve the lookup value from the lookup table and the fine position iscalculated based on the quadrant and the lookup value.

In some embodiments, the method performed by the apparatus 160 using theinstruction 164 stored in the memory 162 also includes generating ascale factor and using the scale factor in the computing of the lookupaddress. The scale factor may be determined iteratively based on one ormore captured local extrema of the first signal and a maximum value ofthe lookup address.

In some embodiments, the method performed by the apparatus 160 using theinstructions 164 stored in the memory 162 also includes receiving asecond signal having a quadrature relationship with the first signalfrom the incremental encoder. The second signal may be received on thesecond input 158. A local maximum and a local minimum of the firstsignal are found and added to produce a sum, which is divided by 2 toproduce a quotient. The first zero-crossing value is then establishedbased on the quotient. The method continues by finding a first localextreme of the first signal at a second time, establishing a secondzero-crossing value based on a value of the second signal at the secondtime, finding a second local extreme of the first signal at a thirdtime, and establishing a fourth zero-crossing value based on a value ofthe second signal at the third time.

The apparatus 160 may include a quadrature-tracking state machine whichis used to update the coarse position. A first indication is provided toa quadrature-tracking state machine based on the first signal crossingthe first zero-crossing value in positive direction, a second indicationis provided to the quadrature-tracking state machine based on the secondsignal crossing the second zero-crossing value in a negative direction,a third indication is provided to the quadrature-tracking state machinebased on the first signal crossing the first zero-crossing value innegative direction, and a fourth indication is provided to thequadrature-tracking state machine based on the second signal crossingthe fourth zero-crossing value in a positive direction. The quadrant ofthe first signal at the first time may be ascertained based on a stateof the quadrature-tracking state machine at the first time.

FIG. 2A shows an example of a rotary encoding disc (or carrier) 110 ofthe rotary incremental encoder 140 of FIG. 1, and FIG. 2B shows andetail of a section 110B of the rotary encoding disc 110 of FIG. 2A. Theview in FIG. 2B is a view of a portion of the carrier 110 looking fromthe right to the left in FIG. 1. The encoder 140 shown utilizes opticaltechnology and the carrier 110 is constructed from an opaque materialwith holes through the carrier 110 used for the encoding elements 220.The encoding elements 220 include a first set of encoding elements 226that includes a hole 126 in a first ring and a second set of encodingelements 228 that includes a hole 128 in a second ring concentric withthe first ring. Both the first set of encoding elements 226 and thesecond set of encoding elements 228 are arranged at the same pitchdistance 230 (i.e. distance apart), but the two sets of encodingelements 226, 228 are offset from each other by a distance 234 equal toone quarter of the pitch distance 230.

The encoder 140 also includes a second opaque element 105 with a slit108 positioned next to the carrier 110 (behind the carrier 110 as shownin FIG. 2B). In other embodiments, the second opaque 105 element mayhave two separate openings corresponding with the first set of encodingelements 226, and the second set of encoding elements 228. The lightsource 102 is located behind the carrier 110 and second opaque element105 in the view shown in FIG. 2B, so that as the carrier 110 moves pastthe slit 108, the carrier 110 selectively allows light to pass throughthe holes in the carrier or blocks the light. In the position shown inFIG. 2B, light 266 is coming through half of hole 126 of the first setof encoding elements 226 (limited by the width of slit 108), and light268 is coming through the full hole 128 of the second set of encodingelements 228 as it is shown aligned with the slit 108.

So looking back to FIG. 1 with FIG. 2B in mind, as the carrier 110 movespast the slit 108, light from the light source 102 is selectivelytransmitted to the light sensors 136, 138. Depending on the embodiment,the voltage level generated by the light sensors 136, 138 used for theencoding elements 220 may be used to generate a sine signal at the firstoutput 146 and a cosine signal at the second output 148 (which have aquadrature relationship) to send to the interpolator 160.

FIG. 3A shows various waveforms 360, 362, 380, 382 and generated values349, 350, 355 of an embodiment. The sine signal 360 may start at azero-crossing value Z 366 and be divided into four quadrants as shown byquadrant indicators 349. The cosine signal 380 has a quadraturerelationship with the sine signal 360 in that it is equivalent to thesine signal 360 except for being shifted to the left by one quadrant(i.e. 90°).

Two digital signals, A 362 and B 382, may be generated from the sinesignal 360 and cosine signal 380, respectively. Signal A 362 may begenerated by comparing the value of the sine signal 360 to thezero-crossing value, Z 366, so that A 362 is high if sine 360 is greaterthan Z 366 and low if sine 360 is less than Z 366. The zero-crossingvalue Z 366 may be determined in some embodiments by finding a localmaximum 361 and a local minimum 363 of the sine signal 360 and averagingthem to determine Z 366. Other embodiments may determine Z 366 usingother techniques.

Similarly, signal B 382 may be generated by comparing the value ofcosine 380 to its own zero-crossing value, which may be determined invarious ways depending on the embodiment. In at least one embodiment,the same zero-crossing value Z 366 may be used for generating the signalB 382 from the cosine signal 380, so that B 382 is high if cosine 380 isgreater than Z 366 and low if cosine 380 is less than Z 366. In otherembodiments, a second zero-crossing value may be determined by finding alocal maximum 381 and a local minimum 383 of the cosine signal 380 andaveraging them to determine the second zero-crossing value to use togenerate B 382. In another embodiment, a local maximum 361 of the sinesignal 360 is found, and a value 371 of the cosine signal 380 at thatsame time is used as the falling zero-crossing value to generate thefalling edge of the signal B 382 from the cosine signal 380.Additionally, a local minimum 363 of the sine signal 360 may be found,and a value 373 of the cosine signal 380 at that same time is used asthe rising zero-crossing value to generate the rising edge of the signalB 382 from the cosine signal 380. In some embodiments, hysteresis may beused in the comparisons to the zero-crossing values to ensure that noiseon the sine signal 360 or cosine signal 380 does not falsely trigger aquadrant change.

FIG. 3B shows a state diagram 300 for an embodiment of aquadrature-tracking state machine. The A signal 362 and the B signal 382may be coupled to the quadrature-tracking state machine and are shown asa two-bit value for AB next to each state transition arrow in the statediagram 300. The embodiment of the quadrature-tracking state machineshown has four states, Q0 390, Q1 310, Q2 320, and Q3 330 whichcorrespond to the quadrants 349 shown in FIG. 3A. Table 1 below showsthe behavior of the embodiment of the quadrature-tracking state machineand its control of a coarse position counter 350 which may increment ordecrement based on quadrant changes.

TABLE 1 Current State A/B Inputs Next State Coarse Position Q0 01 Q3Decrement 11 Q0 Hold 10 Q1 Increment Q1 11 Q0 Decrement 10 Q1 Hold 00 Q2Increment Q2 10 Q1 Decrement 00 Q2 Hold 01 Q3 Increment Q3 00 Q2Decrement 01 Q3 Hold 11 Q0 Increment

In state Q0 390, if AB are 11, the next state 399 is still Q0 390, butif AB are 10, the next state 391 is Q1 310 and the coarse positioncounter is incremented, and if AB are 01, then next state 393 is Q3 330and the coarse position counter is decremented. In state Q1 310, if ABare 10, the next state 311 is still Q1 310, but if AB are 00, the nextstate 312 is Q2 320 and the coarse position counter is incremented, andif AB are 11, then next state 319 is Q0 390 and the coarse positioncounter is decremented. In state Q2 320, if AB are 00, the next state322 is still Q2 320, but if AB are 01, the next state 323 is Q3 330 andthe coarse position counter is incremented, and if AB are 10, then nextstate 321 is Q1 310 and the coarse position counter is decremented. Instate Q3 330, if AB are 01, the next state 333 is still Q3 330, but ifAB are 11, the next state 339 is Q0 390 and the coarse position counteris incremented, and if AB are 00, then next state 332 is Q2 320 and thecoarse position counter is decremented. Note that state transitions areonly provided for three of the four possibilities for AB at each state.The missing combination of AB at each state is not expected and may beignored or treated as an error condition, depending on the embodiment.

Referring back to FIG. 3A, example coarse position values 350 are shownfor an embodiment of the quadrature-tracking state machine shown in FIG.3B and Table 1 based on signal A 362 and signal B 382. The coarseposition counter 350 changes by a single unit to indicate one quarter ofthe movement of the disc of the position encoder required to generate afull cycle of the sine signal 360. Note that the coarse position counter350 increments at the transition 340 from Q0 to Q1, the transition 341from Q1 to Q2, the transition 342 from Q2 to Q3 and the transition 343from Q3 to Q0. But the encoder reverses direction at about time 344 andthe coarse position value 350 decrements at the transition 345 from Q0to Q3.

The fine position value 355 may be calculated using an arcsine value ofa difference between the sine signal S 360 and the zero-crossing value Z366. In some embodiments, a scaling factor may be used so that thedifference between Z 366 and the local maximum 361 and local minimum 363values is equal to 1 so that the arcsine function does not have adiscontinuity at quadrant transitions. Note that the multiplication bythe scaling factor is not shown in the equation for the sake ofsimplicity. The way that the fine position value 355 is calculatedvaries by quadrant with the zero-crossing value 366 being subtractedfrom the sine value 360 in Q0 and Q1 and the sine value 360 subtractedfrom the zero-crossing value 366 in Q2 and Q3 so that a positivedifference is always calculated. The difference (which may be multipliedby a scaling factor) is then used as an address into a lookup tablehaving arcsine values stored therein. In the embodiment shown, all ofthe arcsine values stored in the table are scaled between 0 and 1 (i.e.the radix is assumed to be to the left of the stored value) with alookup value of 0 may access a location holding all 0s and the maximumlookup address for the table may access a location holding all 1s. Anynumber of bits may be stored in the lookup table, depending on theembodiment, but 16 bits of arcsine date may be stored in the lookuptable in at least one embodiment.

The arcsine data from the lookup table may be directly used as the fineposition in Q0 and Q2, but in Q1 and Q3, the arcsine data is subtractedfrom a constant that may be the increment between coarse position values(e.g. a 1 in the embodiment shown) to generate the fine position. Thefine position is then added to the coarse position to generate theinterpolated position of the encoder.

FIG. 4 is a block diagram of an embodiment of an apparatus 400 toprovide an interpolated position of an incremental encoder. Theapparatus includes at least one input 411, 412 configured to receivefirst information related to a first signal and second informationrelated to a second signal. In the embodiment shown the at least oneinput includes a first analog input 411 and a second analog input 412coupled to respective inputs of one or more analog-to-digital converters413, 414 which may provide the first information on a first output 415and the second information on a second output 416. In other embodiments,the at least one input may include a first digital input to receive thefirst information and a second digital input to receive the secondinformation or a single digital interface configured to demultiplex thefirst information from the second information. Any of the digitalinterfaces may be a parallel interface or a serial interface and thefirst information and the second information both may include digitalvalues having any number of bits of information, such as, but notlimited to, 4, 8, 12, or 16 bits of information

The apparatus 400 also includes a quadrature state machine 420 coupledto the at least one input 411, 412 and configured to track a quadraturerelationship of the first signal and the second signal using a statemachine such as that shown in FIG. 3B. The quadrature state machine 420provides a quadrant output 422 and counter control lines 424. A coarseposition counter 430 is also included in the apparatus 400. The coarseposition counter 430 is coupled to the counter control lines 424 and isconfigured to increment and decrement under control of the quadraturestate machine 420.

The apparatus may also include quadrant determination circuitry 490coupled to the at least one input 411, 412 and configured to provide azero-crossing value for the second information on a second zero-crossingoutput 497. A first comparator 494 is coupled to the first output 415and a first zero-crossing output 457 with its output coupled to thequadrature state machine 420 and a second comparator 492 is coupled tothe second output 416 and the second zero-crossing output 497 with itsoutput coupled to the quadrature state machine 420. The quadrantdetermination circuitry 490 may further include circuitry to detect afirst local extreme of the first information at a second time anddetermine the zero-crossing value for the second information based on afirst value of the second information at the second time, and detect asecond local extreme of the first information at a third time anddetermine the zero-crossing value for the second information based on asecond value of the second information at the third time.

Address calculation circuitry 440 is also included in the apparatus 400.It is coupled to the at least one input 411 and the quadrant output 422of the quadrature state machine 420 and is configured to generate alookup address output 459. The address calculation circuitry 440 alsomay include zero-crossing circuitry 450 to provide a zero-crossing valuefor the first information on the first zero-crossing output 457. Thezero-crossing circuitry 450 may also be configured to capture a localmaximum 451 and a local minimum 452 of the first information provided bythe first output 415 and provide a local maximum output and a localminimum output to an adder 454. The output of the adder 454 may beshifted to divide by 2 (calculating an average of the local maximum 451and the local minimum 452) and provided to a subtraction circuit 455which is also coupled to the first output 415.

Some embodiments may also include a scaler calculation state machine 445configured to iteratively determine a scale factor based on one or morecaptured local extrema of the first information and a maximum value ofthe lookup address for the lookup table and provide the scale factor onan output. A multiplier 456 may be coupled to an output of thesubtraction circuit 455 and the output of the scaler state machine 445.The output of the multiplier 456 is coupled to the memory 460 as thelookup address output 459.

A memory 460 having an address input 462 coupled to the lookup addressoutput 459 is also included in the apparatus 400. The memory 460 maystore a lookup table holding values based on an arcsine or an arccosineof a value of the lookup address output 459 in some embodiments. Thelookup address output 459 may be interpreted as a number between 0 and 1for the purposes of looking up the arcsine value in the lookup table460.

The apparatus 400 also includes circuitry 470 to generate theinterpolated position 409 of the incremental encoder based on both anoutput of the coarse position counter 430 and an output 464 of thememory 460. The circuitry 470 may also generate an offset value 476 thatmay be equal to an increment of the coarse counter 430 and may providethe offset value 476 to the coarse position counter as theincrement/decrement value in some embodiments. A subtraction circuit 472may be coupled to the output 464 of the memory 460 and the offset value476 which may be controlled based on the quadrant output 422 of thequadrant state machine 420 to subtract the output 464 of the memory 460from the offset 476 in Q1 and Q3 and simply pass the output 464 of thememory 460 to the adder 474 in Q0 and Q2. The adder 474 adds the outputof the subtraction circuit 472 to the output of the coarse positioncounter 430 to generate the interpolated position 409 of the incrementalencoder. In some embodiments, the coarse position counter 430 output isused as the whole number information to the left of the radix, and thefine position (i.e. the output of the subtraction circuit 472) is usesas the fractional information to the right of the radix, so the adder474 simply appends the bits together instead of implementing a fulladder circuit. Thus, the interpolated position 490 of the incrementalencoder may be based on the output of the coarse position counter 430and an output of the subtraction circuit 472.

Aspects of various embodiments are described with reference to flowchartillustrations and/or block diagrams of methods, apparatus, systems, andcomputer program products according to various embodiments disclosedherein. It will be understood that various blocks of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions or by configuration information for afield-programmable gate array (FPGA). These computer programinstructions may be provided to a processor of a general purposecomputer, special purpose computer, or other programmable dataprocessing apparatus to produce a machine, such that the instructions,which execute via the processor of the computer or other programmabledata processing apparatus, create means for implementing thefunctions/acts specified in the flowchart and/or block diagram block orblocks. Similarly, the configuration information for the FPGA may beprovided to the FPGA and configure the FPGA to produce a machine whichcreates means for implementing the functions/acts specified in theflowchart and/or block diagram block or blocks.

These computer program instructions or FPGA configuration informationmay be stored in a computer readable medium that can direct a computer,other programmable data processing apparatus, FPGA, or other devices tofunction in a particular manner, such that the data stored in thecomputer readable medium produce an article of manufacture includinginstructions which implement the function/act specified in the flowchartand/or block diagram block or blocks. The computer program instructionsor FPGA configuration information may also be loaded onto a computer,FPGA, other programmable data processing apparatus, or other devices tocause a series of operational steps to be performed on the computer,FPGA, other programmable apparatus, or other devices to produce acomputer implemented process for implementing the functions/actsspecified in the flowchart and/or block diagram block or blocks.

The flowchart and/or block diagrams in the figures help to illustratethe architecture, functionality, and operation of possibleimplementations of systems, methods and computer program products ofvarious embodiments. In this regard, each block in the flowchart orblock diagrams may represent a module, segment, or portion of codecomprising one or more executable instructions, or a block of circuitry,for implementing the specified logical function(s). It should also benoted that, in some alternative implementations, the functions noted inthe block may occur out of the order noted in the figures. For example,two blocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

FIG. 5A is a flowchart 500 of an embodiment of a method to provide aninterpolated position 501 of an incremental encoder. A first signal isreceived 503 from the incremental encoder and a coarse position of theincremental encoder is produced 510 based on the first signal. FIG. 5Bprovides more detail into how the coarse position of the incrementalencoder is produced 510. In embodiments the coarse position may have aresolution that is no finer than one eighth of a cycle of the firstsignal, such as one cycle of the first signal, one half cycle of thefirst signal, or one quarter cycle of the first signal.

The flowchart 500 continues by retrieving 520 a lookup value from alookup table based on the first signal. The lookup table may storevalues based on an arcsine or an arccosine of a value of the lookupaddress with the value of the lookup address interpreted as a numberbetween 0 and 1. FIG. 5C-5F provide more detail into how the lookupvalue is retrieved 520 from the lookup table based on the first signal.A fine position of the incremental encoder is calculated 590 using thelookup value. FIG. 5G provides more detail into how the fine position ofthe incremental encoder is calculated 590. The flowchart 500 thenprovides 599 an interpolated position of the incremental encoder basedon both the coarse position and the fine position and repeats.

FIG. 5B is a flowchart 510B providing more detail for producing 510 acoarse position of the flowchart 500 of FIG. 5A. A second signal isreceived 511 from the incremental encoder. The first signal and thesecond signal have a quadrature relationship which is tracked 512; inembodiments the first signal may be a sine signal and the second signalmay be a cosine signal. A state machine in accordance with FIG. 3B abovemay be used to track 512 the quadrature relationship of the two signals.Other techniques to track 512 the quadrature relationship between thetwo signals may be used in other embodiments.

The tracking 512 of the quadrature relationship between the first signaland the second signal may be used to produce the coarse position of theincremental encoder. In some embodiments, one or more outputs of thequadrature-tracking state machine may be used to update the coarseposition. If the quadrant changes 514 in an upward direction, that isQ0→Q1, Q1→Q2, Q2→Q3, or Q3→Q0, the coarse counter may be incremented517. If the coarse position has a resolution of one quarter of a cycleof the first signal, it is incremented 517 at every upward quadrantchange, but if a lower resolution is used, the incrementing 517 may onlyoccur at some of the upward quadrant changes. If the quadrant changes514 in a downward direction, that is Q0→Q3, Q1→Q0, Q2→Q1, or Q3→Q2, thecoarse counter may be decremented 516. If the coarse position has aresolution of one quarter of a cycle of the first signal, it isdecremented 516 at every downward quadrant change, but if a lowerresolution is used, the decrementing 516 may only occur at some of thedownward quadrant changes. A current quadrant indicator and the value ofthe coarse counter may be provided 519.

In some embodiments, the first signal and second signal may be comparedto one or more zero-crossing values to determine that the quadrant ofthe first signal has changed 514. In at least one embodiment, a firstindication of a quadrant change 514 is provided to a quadrature-trackingstate machine based on the first signal crossing the first zero-crossingvalue in positive direction, a second indication of a quadrant change514 is provided to the quadrature-tracking state machine based on thesecond signal crossing a second zero-crossing value in a negativedirection, a third indication of a quadrant change 514 is provided tothe quadrature-tracking state machine based on the first signal crossinga third zero-crossing value in negative direction, and a fourthindication of a quadrant change 514 is provided to thequadrature-tracking state machine based on the second signal crossing afourth zero-crossing value in a positive direction. The quadrant of thefirst signal may be ascertained based on a state of thequadrature-tracking state machine.

In some embodiments, all four of the zero-crossing values may be set tothe same value, but in other embodiments, two, three, or four differentzero-crossing values may be used for the four different zero-crossingvalues. In some embodiments, the first zero-crossing value may be foundas shown in flowchart 530D of FIG. 5D (described below) and the thirdzero-crossing value may be set to the first zero-crossing value, but inother embodiments, the third zero-crossing value may be setindependently from the first zero-crossing value. In at least oneembodiment the second zero-crossing value may be set by finding a firstlocal extreme of the first signal at a second time and setting thesecond zero-crossing value based on a value of the second signal at thesecond time and the fourth zero-crossing value may be set by finding asecond local extreme of the first signal at a third time and setting thefourth zero-crossing value based on a value of the second signal at thethird time.

FIG. 5C is a flowchart 520C providing more detail for retrieving 520 alookup value of the flowchart 500 of FIG. 5A. A first zero-crossingvalue for the first signal is established 530 and a digital value of thefirst signal at a first time is obtained. FIG. 5D provides more detailinto how the first zero-crossing value for the first signal isestablished 530. A lookup address is computed 550 based on a differencebetween the digital value and the first zero-crossing value. FIG. 5Eprovides more detail into how the lookup address is computed 550. Insome embodiments, a larger value and a smaller value is determinedbetween the digital value and the first zero-crossing value and thesmaller value is subtracted from the larger value to compute the lookupaddress. The lookup address is then used 588 to retrieve the lookupvalue from the lookup table and the fine position is calculated based onthe quadrant and the lookup value.

FIG. 5D is a flowchart 530D providing more detail for establishing 530 afirst zero-crossing value of the flowchart 520C of FIG. 5C. A localmaximum of the first signal is found 532 and a local minimum of thefirst signal is also found 534. This establishes a value range of thefirst signal at least for a portion of range of movement for theincremental encoder. An average of the local maximum and local minimumis calculated 536 by adding the local maximum to the local minimum toproduce a sum and shifting the sum by 1 bit position to produce aquotient. Other techniques to calculate an average may be used by otherembodiments. The first zero-crossing value is then established 538 basedon the quotient. Some embodiments may dynamically calculate the firstzero-crossing value for each new cycle of the first signal while otherembodiments, may calculate the first zero-crossing value over a range ofmotion of the incremental encoder and then use the value until a resetoccurs or a new calibration command is received.

FIG. 5E is a flowchart 550E providing more detail for computing 550 alookup address of the flowchart 520C of FIG. 5C. A quadrant of the firstsignal at the first time is ascertained 552. An indication of thecurrent quadrant may be provided by a quadrature-tracking state machine.The ascertained quadrant is evaluated 554 to determine if the quadrantis in a first half of a cycle of the first signal (i.e. Q0 or Q1). If itis in the first half cycle, then the first zero-crossing value issubtracted 558 from the digital value of the first signal, but if it isin the second half cycle (i.e. Q2 or Q3) the digital value of the firstsignal is subtracted 556 from the first zero-crossing value. In someembodiments, a scale factor is then obtained 560 and the scale factor ismultiplied 586 by the calculated difference between the digital valueand the first zero-crossing value to compute the lookup address. Thescale factor may be obtained using an iterative approach based on one ormore captured local extrema of the first signal and a maximum value ofthe lookup address.

FIG. 5F is a flowchart 560F providing more detail for obtaining 560 ascale factor of the flowchart 550E of FIG. 5E. The first signal ismonitored 562 over a time period preceding the first time to obtain 564one or more local extrema values. In at least one embodiment, the one ormore local extrema values consist of a single local extrema value thatis captured at a second time, prior to the first time, the second timedetermined by a change of a quadrant of the first signal. In anotherembodiment the one or more local extrema values consist of between 2 and32 local extrema values. A pre-scaled maximum value (X) is obtainedfinding 566 a maximum of absolute values of differences between thefirst zero-crossing value and the one or more local extrema values toobtain a pre-scaled maximum value. A trial scale factor is obtained 568and the pre-scaled maximum value is multiplied 572 by the trial scalefactor by to obtain a scaled maximum value.

A difference value is obtained by subtracting the scaled maximum valuefrom the maximum value for the lookup address and evaluated to decide574 if it is in a predetermined range. The trial scale factor is changed(i.e. updated) 576 by an amount based on the difference value inresponse to the difference value being outside of the predeterminedrange and used to multiply the pre-scaled maximum value 572 to beevaluated again. This is repeated until the difference value is withinthe predetermined range. The scale factor is then set 578 to the trialscale factor in response to the difference value being within thepredetermined range. So the scale factor may be generated based on amaximum of absolute values of differences between the one or more localextrema values and the first zero-crossing value for the first signal.

In an embodiment the first signal may be monitored over a portion of arange of motion of the incremental encoder to obtain a maximum of anabsolute value of differences between values of the first signal overthe portion of the range of motion and the first zero-crossing value.The scale factor may then be generated based on a maximum value for thelookup address and the maximum of the absolute value of said differencesbetween the values of the first signal over the portion of the range ofmotion and the first zero-crossing value.

In a somewhat different embodiment, the scale factor (scale) isgenerated based on a maximum value for the lookup address (Amax), aguard band value (A), the one or more (n) local extrema values (l_(i))and the first zero-crossing value (Z) for the first signal, by use ofthe following equation:

${scale} = {\frac{{A\mspace{11mu}\max} - \Delta}{\max\left( {{Z - l_{{i:i} = {1\rightarrow n}}}} \right)}.}$

In various embodiments the guard band value (A) may have a value between0 and 16 times a value of a least significant bit of Amax or a negativevalue.

FIG. 5G is a flowchart 590G providing more detail for calculating 590 afine position of the flowchart 500 of FIG. 5A. An offset is obtained 591which may be set to a predetermined constant value such as theresolution of the coarse position counter. In some embodiments theoffset may have a value of 1. A quadrant of the first signal isascertained and if the quadrant of the first signal at the first time isQ1 or Q3 592, the fine position is determined 593 based on subtractingthe lookup value retrieved from a lookup table from the offset. Thelookup table may store values based on an arcsine of a value of thelookup address, wherein the value of the lookup address is interpretedas a number between 0 and 1. If the quadrant is Q0 or Q2 592, the fineposition is determined 594 based on the lookup value without using theoffset.

In some embodiments, a fine scaling factor is obtained 596, which may beequal to 1 or the resolution of the coarse position counter. The fineposition may be multiplied 597 by the fine scaling factor to calculatefinal fine position. So in at least one embodiment, the fine positionmay be calculated as a product of the fine scaling factor and the lookupvalue in response the ascertaining that the quadrant is Q0 or Q2 whichare characterized by the first signal and the second signal being on asame side of the first zero-crossing value and the second zero-crossingvalue, respectively, and the fine position is calculated as a product ofthe fine scaling factor and a result of subtracting the lookup valuefrom a constant value in response the ascertaining that the quadrant isQ1 or Q3 which are characterized by the first signal and the secondsignal being on opposite sides of the first zero-crossing value and thesecond zero-crossing value, respectively.

As will be appreciated by those of ordinary skill in the art, aspects ofthe various embodiments may be embodied as a system, device, method, orcomputer program product apparatus. Accordingly, elements of the presentdisclosure may take the form of an entirely hardware embodiment, anentirely software embodiment (including firmware, resident software,micro-code, or the like) or an embodiment combining software andhardware aspects that may all generally be referred to herein as a“apparatus,” “server,” “circuitry,” “module,” “client,” “computer,”“logic,” “FPGA,” “system,” or other terms. Furthermore, aspects of thevarious embodiments may take the form of a computer program productembodied in one or more computer-readable medium(s) having computerprogram code stored thereon. The phrases “computer program code” and“instructions” both explicitly include configuration information for anFPGA or other programmable logic as well as traditional binary computerinstructions, and the term “processor” explicitly includes logic in anFPGA or other programmable logic configured by the configurationinformation in addition to a traditional processing core. Furthermore,“executed” instructions explicitly includes electronic circuitry of anFPGA or other programmable logic performing the functions for which theyare configured by configuration information loaded from a storage mediumas well as serial or parallel execution of instructions by a traditionalprocessing core.

Any combination of one or more computer-readable storage medium(s) maybe utilized. A computer-readable storage medium may be embodied as, forexample, an electronic, magnetic, optical, electromagnetic, infrared, orsemiconductor system, apparatus, or device, or other like storagedevices known to those of ordinary skill in the art, or any suitablecombination of computer-readable storage mediums described herein. Inthe context of this document, a computer-readable storage medium may beany tangible medium that can contain, or store a program and/or data foruse by or in connection with an instruction execution system, apparatus,or device. Even if the data in the computer-readable storage mediumrequires action to maintain the storage of data, such as in atraditional semiconductor-based dynamic random access memory, the datastorage in a computer-readable storage medium can be considered to benon-transitory. A computer data transmission medium, such as atransmission line, a coaxial cable, a radio-frequency carrier, and thelike, may also be able to store data, although any data storage in adata transmission medium can be said to be transitory storage.Nonetheless, a computer-readable storage medium, as the term is usedherein, does not include a computer data transmission medium.

Computer program code for carrying out operations for aspects of variousembodiments may be written in any combination of one or more programminglanguages, including object oriented programming languages such as Java,Python, C++, or the like, conventional procedural programming languages,such as the “C” programming language or similar programming languages,or low-level computer languages, such as assembly language or microcode.In addition, the computer program code may be written in VHDL or anotherhardware description language to generate configuration instructions foran FPGA or other programmable logic. The computer program code ifconverted into an executable form and loaded onto a computer, FPGA, orother programmable apparatus, produces a computer implemented method.The instructions which execute on the computer, FPGA, or otherprogrammable apparatus may provide the mechanism for implementing someor all of the functions/acts specified in the flowchart and/or blockdiagram block or blocks. In accordance with various implementations, thecomputer program code may execute entirely on the user's device, partlyon the user's device and partly on a remote device, or entirely on theremote device, such as a cloud-based server. In the latter scenario, theremote device may be connected to the user's device through any type ofnetwork, including a local area network (LAN) or a wide area network(WAN), or the connection may be made to an external computer (forexample, through the Internet using an Internet Service Provider). Thecomputer program code stored in/on (i.e. embodied therewith) thenon-transitory computer-readable medium produces an article ofmanufacture.

The computer program code, if executed by a processor, causes physicalchanges in the electronic devices of the processor which change thephysical flow of electrons through the devices. This alters theconnections between devices which changes the functionality of thecircuit. For example, if two transistors in a processor are wired toperform a multiplexing operation under control of the computer programcode, if a first computer instruction is executed, electrons from afirst source flow through the first transistor to a destination, but ifa different computer instruction is executed, electrons from the firstsource are blocked from reaching the destination, but electrons from asecond source are allowed to flow through the second transistor to thedestination. So a processor programmed to perform a task is transformedfrom what the processor was before being programmed to perform thattask, much like a physical plumbing system with different valves can becontrolled to change the physical flow of a fluid.

Examples of various embodiments are described in the followingparagraphs:

Embodiment 1. A method to provide an interpolated position of anincremental encoder, the method comprising: receiving a first signal anda second signal from the incremental encoder, the first signal and thesecond signal having a quadrature relationship; producing a coarseposition of the incremental encoder at a first time using the quadraturerelationship between the first signal and the second signal; determiningan arcsine or arccosine value based on the first signal at the firsttime; calculating a fine position of the incremental encoder using thedetermined arcsine or arccosine value; and providing the interpolatedposition of the incremental encoder at the first time based on both thecoarse position and the fine position.

Embodiment 2. A method to provide an interpolated position of anincremental encoder, the method comprising: receiving a first signalfrom the incremental encoder; producing a coarse position of theincremental encoder based on the first signal; retrieving a lookup valuefrom a lookup table based on the first signal; calculating a fineposition of the incremental encoder using the lookup value; andproviding the interpolated position of the incremental encoder based onboth the coarse position and the fine position.

Embodiment 3. The method of embodiment 2, wherein the lookup tablestores values based on an arcsine or an arccosine of a value of thelookup address, wherein the value of the lookup address is interpretedas a number between 0 and 1.

Embodiment 4. The method of embodiment 2 or 3, wherein the coarseposition has a resolution no finer than one eighth of a cycle of thefirst signal.

Embodiment 5. The method of any of embodiments 2-4, wherein the coarseposition has a resolution of one cycle of the first signal, one halfcycle of the first signal, or one quarter cycle of the first signal.

Embodiment 6. The method of any of embodiments 2-5, further comprising:receiving a second signal from the incremental encoder, the first signaland the second signal having a quadrature relationship; and producingthe coarse position of the incremental encoder using the quadraturerelationship between the first signal and the second signal.

Embodiment 7. The method of embodiment 6, wherein the first signal andthe second signal are analog signals provided at two separate inputs.

Embodiment 8. The method of embodiment 6, wherein the first signal andthe second signal comprise a first set of digital values and a secondset of digital values.

Embodiment 9. The method of embodiment 8, wherein a value in the firstset of digital values or the second set of digital values consists of 4,8, 12, or 16 bits of information.

Embodiment 10. The method of embodiment 8 or 9, wherein the first set ofdigital values is received on a first serial interface and the secondset of digital values is received on a second serial interface.

Embodiment 11. The method of embodiment 8 or 9, wherein the first set ofdigital values is received on a first parallel interface and the secondset of digital values is received on a second parallel interface.

Embodiment 12. The method of embodiment 8 or 9, wherein the first set ofdigital values and the second set of digital values are received on acommon serial interface.

Embodiment 13. The method of embodiment 8 or 9, wherein the first set ofdigital values and the second set of digital values are received on acommon parallel interface.

Embodiment 14. The method of any of embodiments 2-13, furthercomprising:

establishing a first zero-crossing value for the first signal; obtaininga digital value of the first signal at a first time; ascertaining aquadrant of the first signal at the first time; computing a lookupaddress based on a difference between the digital value and the firstzero-crossing value; using the lookup address to retrieve the lookupvalue from the lookup table; and calculating the fine position based onthe quadrant and the lookup value.

Embodiment 15. The method of embodiment 14, wherein the lookup tablestores values based on an arcsine of a value of the lookup address,wherein the value of the lookup address is interpreted as a numberbetween 0 and 1.

Embodiment 16. The method of embodiment 14 or 15, further comprising:determining a larger value and a smaller value between the digital valueand the first zero-crossing value; and subtracting the smaller valuefrom the larger value to compute the lookup address.

Embodiment 17. The method of embodiment 14 or 15, the computing thelookup address comprising: computing the lookup address by subtractingthe first zero-crossing value from the digital value in response to theascertaining that the quadrant of the first signal at the first time isin a first half of a cycle of the first signal; and computing the lookupaddress by subtracting the digital value from the first zero-crossingvalue in response to the ascertaining that the quadrant of the firstsignal at the first time is in a second half of the cycle of the firstsignal.

Embodiment 18. The method of any of embodiments 14-17, the calculatingthe fine position comprising subtracting the lookup value from an offsetvalue in response to the ascertaining that the quadrant of the firstsignal at the first time is Q1 or Q3.

Embodiment 19. The method of embodiment 18, wherein the offset value isa predetermined constant value.

Embodiment 20. The method of any of embodiments 14-19, furthercomprising:

receiving a second signal from the incremental encoder, the first signaland the second signal having a quadrature relationship; establishing asecond zero-crossing value for the second signal; obtaining a finescaling factor; calculating the fine position based on a product of thefine scaling factor and the lookup value in response the ascertainingthat the quadrant of the first signal at the first time is characterizedby the first signal and the second signal being on a same side of thefirst zero-crossing value and the second zero-crossing value,respectively; and calculating the fine position based on a product ofthe fine scaling factor and a result of subtracting the lookup valuefrom a constant value in response the ascertaining that the quadrant ofthe first signal at the first time is characterized by the first signaland the second signal being on opposite sides of the first zero-crossingvalue and the second zero-crossing value, respectively.

Embodiment 21. The method of embodiment 20, wherein the fine scalingfactor is equal to 1 and the constant value is equal to 1.

Embodiment 22. The method of any of embodiments 14-21, furthercomprising: finding a local maximum of the first signal; finding a localminimum of the first signal; computing an average of the local maximumand the local minimum; and establishing the first zero-crossing valuebased on the average.

Embodiment 23. The method of any of embodiments 14-22, the methodfurther comprising: receiving a second signal from the incrementalencoder, the first signal and the second signal having a quadraturerelationship; providing a first indication to a quadrature-trackingstate machine based on the first signal crossing the first zero-crossingvalue in positive direction; providing a second indication to thequadrature-tracking state machine based on the second signal crossing asecond zero-crossing value in a negative direction; providing a thirdindication to the quadrature-tracking state machine based on the firstsignal crossing a third zero-crossing value in negative direction;providing a fourth indication to the quadrature-tracking state machinebased on the second signal crossing a fourth zero-crossing value in apositive direction; updating the coarse position based on an output ofthe quadrature-tracking state machine; and ascertaining the quadrant ofthe first signal at the first time based on a state of thequadrature-tracking state machine at the first time.

Embodiment 24. The method of embodiment 23, the second zero-crossingvalue, the third zero-crossing value, and the fourth zero-crossing valuebeing equal to the first zero-crossing value.

Embodiment 25. The method of embodiment 23, further comprising: findinga first local extreme of the first signal at a second time; setting thesecond zero-crossing value based on a value of the second signal at thesecond time; finding a second local extreme of the first signal at athird time; and setting the fourth zero-crossing value based on a valueof the second signal at the third time.

Embodiment 26. The method of any of embodiments 14-25, furthercomprising:

generating a scale factor; and using the scale factor in the computingof the lookup address.

Embodiment 27. The method of embodiment 26, further comprisingdetermining the scale factor iteratively based on one or more capturedlocal extrema of the first signal and a maximum value of the lookupaddress.

Embodiment 28. The method of embodiment 26 or 27, further comprisingmultiplying the scale factor by the difference between the digital valueand the first zero-crossing value to compute the lookup address.

Embodiment 29. The method of embodiment 26 or 28, further comprising:monitoring the first signal over a portion of a range of motion of theincremental encoder to obtain a maximum of an absolute value ofdifferences between values of the first signal over the portion of therange of motion and the first zero-crossing value; and generating thescale factor based on a maximum value for the lookup address and themaximum of the absolute value of the differences between the values ofthe first signal over the portion of the range of motion and the firstzero-crossing value.

Embodiment 30. The method of embodiment 26 or 28, further comprising:monitoring the first signal over a time period preceding the first timeto obtain one or more local extrema values; and generating the scalefactor based on a maximum value for the lookup address and the one ormore local extrema values.

Embodiment 31. The method of embodiment 30, wherein the one or morelocal extrema values consist of a single local extrema value that iscaptured at a second time, prior to the first time, the second timedetermined by a change of the quadrant of the first signal.

Embodiment 32. The method of embodiment 30 or 31, further comprising:(a) obtaining a trial scale factor; (b) finding a maximum of absolutevalues of differences between the first zero-crossing value and the oneor more local extrema values to obtain a pre-scaled maximum value; (c)multiplying the trial scale factor by the pre-scaled maximum value toobtain a scaled maximum value; (d) subtracting the scaled maximum valuefrom the maximum value for the lookup address to obtain a differencevalue; (e) changing the trial scale factor by an amount based on thedifference value in response to the difference value being outside of apredetermined range, and repeating (c), (d), and (e) until thedifference value is within the predetermined range; and (f) setting thescale factor to the trial scale factor in response to the differencevalue being within the predetermined range.

Embodiment 33. The method of embodiment 30, wherein the one or morelocal extrema values consist of between 2 and 32 local extrema values,and the scale factor is generated based on a maximum of absolute valuesof differences between the one or more local extrema values and thefirst zero-crossing value for the first signal.

Embodiment 34. The method of embodiment 30, wherein the scale factor(scale) is generated based on a maximum value for the lookup address(Amax), a guard band value (Δ), the one or more (n) local extrema values(l_(i)) and the first zero-crossing value (Z) for the first signal, byuse of the following equation:

${scale} = {\frac{{A\;\max} - \Delta}{\max\left( {{Z - l_{{ii} = {1\rightarrow n}}}} \right)}.}$

Embodiment 35. The method of embodiment 34, wherein the guard band value(Δ) has a value between 0 and 16 times a value of a least significantbit of Amax, inclusive.

Embodiment 36. The method of embodiment 34 or 35, wherein the guard bandvalue (Δ) has a negative value.

Embodiment 37. An article of manufacture comprising a non-transitorystorage medium having instructions stored thereon that, if executed,result in: receiving a first signal from an incremental encoder;producing a coarse position of the incremental encoder based on thefirst signal; retrieving a lookup value from a lookup table based on thefirst signal; calculating a fine position of the incremental encoderusing the lookup value; and providing an interpolated position of theincremental encoder based on both the coarse position and the fineposition.

Embodiment 38. The article of manufacture of embodiment 37, wherein theinstructions, if executed, further result in: establishing a firstzero-crossing value for the first signal; obtaining a digital value ofthe first signal at a first time; ascertaining a quadrant of the firstsignal at the first time; computing a lookup address based on adifference between the digital value and the first zero-crossing value;using the lookup address to retrieve the lookup value from the lookuptable; and calculating the fine position based on the quadrant and thelookup value.

Embodiment 39. The article of manufacture of embodiment 38, wherein theinstructions, if executed, further result in: generating a scale factor;and using the scale factor in the computing of the lookup address.

Embodiment 40. The article of manufacture of embodiment 39, wherein theinstructions, if executed, further result in determining the scalefactor iteratively based on one or more captured local extrema of thefirst signal and a maximum value of the lookup address.

Embodiment 41. The article of manufacture of any of embodiments 38-40,wherein the instructions, if executed, further result in: receiving asecond signal from the incremental encoder, the first signal and thesecond signal having a quadrature relationship; finding a local maximumof the first signal at a second time; finding a local minimum of thefirst signal at a third time; computing an average of the local maximumand the local minimum; establishing the first zero-crossing value basedon the average; establishing a second zero-crossing value based on avalue of the second signal at the second time; establishing a thirdzero-crossing value based on a value of the second signal at the thirdtime; providing a first indication to a quadrature-tracking statemachine based on the first signal crossing the first zero-crossing valuein positive direction; providing a second indication to thequadrature-tracking state machine based on the second signal crossingthe second zero-crossing value in a negative direction; providing athird indication to the quadrature-tracking state machine based on thefirst signal crossing the first zero-crossing value in negativedirection; providing a fourth indication to the quadrature-trackingstate machine based on the second signal crossing the thirdzero-crossing value in a positive direction; updating the coarseposition based on an output of the quadrature-tracking state machine;and ascertaining the quadrant of the first signal at the first timebased on a state of the quadrature-tracking state machine at the firsttime.

Embodiment 42. An apparatus to provide an interpolated position of anincremental encoder, the apparatus comprising: at least one inputconfigured to receive first information related to a first signal andsecond information related to a second signal; a quadrature statemachine coupled to the at least one input and configured to track aquadrature relationship of the first signal and the second signal, thequadrature state machine providing a quadrant output and counter controllines; a coarse position counter coupled to the counter control linesand configured to increment and decrement under control of thequadrature state machine; address calculation circuitry, coupled to theat least one input and the quadrant output of the quadrature statemachine, and configured to generate a lookup address output; a memoryhaving an address input coupled to the lookup address output; andcircuitry to generate the interpolated position of the incrementalencoder based on both an output of the coarse position counter and anoutput of the memory.

Embodiment 43. The apparatus of embodiment 42, wherein the memory storesa lookup table comprising values based on an arcsine or an arccosine ofa value of the lookup address output, wherein the lookup address outputis interpreted as a number between 0 and 1.

Embodiment 44. The apparatus of embodiment 42 or 43, further comprisingone or more analog-to-digital converters, wherein the at least one inputcomprises a first analog input and a second analog input coupled torespective inputs of the one or more analog-to-digital converters.

Embodiment 45. The apparatus of embodiment 42 or 43, wherein the atleast one input comprises a first digital input to receive the firstinformation and a second digital input to receive the secondinformation.

Embodiment 46. The apparatus of embodiment 45, wherein the first digitalinput comprises a first serial interface, and the second digital inputcomprises a second serial interface.

Embodiment 47. The apparatus of embodiment 45, wherein the first digitalinput comprises a first parallel interface, and the second digital inputcomprises a second parallel interface.

Embodiment 48. The apparatus of embodiment 42 or 43, wherein the atleast one input consists of a single digital interface configured todemultiplex the first information from the second information.

Embodiment 49. The apparatus of embodiment 48, wherein the firstinformation and the second information both comprise digital valuesconsisting of 4, 8, 12, or 16 bits of information.

Embodiment 50. The apparatus of embodiment 48 or 49, wherein the singledigital interface consists of a serial interface.

Embodiment 51. The apparatus of embodiment 48 or 49, wherein singledigital interface consists of a parallel interface.

Embodiment 52. The apparatus of any of embodiments 42-51, furthercomprising: circuitry to generate an offset value at an offset output;and a subtraction circuit coupled to the output of the memory and theoffset output; wherein the interpolated position of the incrementalencoder is based on both the output of the coarse position counter andan output of the subtraction circuit.

Embodiment 53. The apparatus of any of embodiments 42-51, furthercomprising: circuitry coupled to the at least one input and configuredto provide the first information on a first output; circuitry coupled tothe first output and configured to provide a zero-crossing value for thefirst information on a zero-crossing output; and a subtraction circuitcoupled to the first output and the zero-crossing output, an output ofthe subtraction circuit coupled to the lookup address output.

Embodiment 54. The apparatus of any of embodiments 42-53, furthercomprising: circuitry coupled to the at least one input and configuredto provide the first information on a first output; circuitry coupled tothe first output and configured to capture a local maximum and a localminimum of the first information and provide a local maximum output anda local minimum output; an adder coupled to the local maximum output andthe local minimum output; a subtraction circuit coupled to the firstoutput and an output of the adder; and a multiplier coupled to an outputof the subtraction circuit and a scaler output, an output of themultiplier coupled to the memory as the lookup address output.

Embodiment 55. The apparatus of embodiment 54, further comprising ascaler calculation state machine configured to: iteratively determine ascale factor based on one or more captured local extrema of the firstinformation and a maximum value of the lookup address for the lookuptable; and provide the scale factor on the scaler output.

Embodiment 56. The apparatus of any of embodiments 42-55, furthercomprising: circuitry coupled to the at least one input and configuredto provide the first information on a first output, the secondinformation on a second output, a zero-crossing value for the firstinformation on a first zero-crossing output, and a zero-crossing valuefor the second information on a second zero-crossing output; a firstcomparator coupled to the first output and the first zero-crossingoutput, an output of the first comparator coupled to the quadraturestate machine; and a second comparator coupled to the second output andthe second zero-crossing output, an output of the second comparatorcoupled to the quadrature state machine.

Embodiment 57. The apparatus of embodiment 56, further comprisingcircuitry to: detect a first local extreme of the first information at asecond time and determine the zero-crossing value for the secondinformation based on a first value of the second information at thesecond time; and detect a second local extreme of the first informationat a third time and determine the zero-crossing value for the secondinformation based on a second value of the second information at thethird time.

Embodiment 58. At least one non-transitory machine readable mediumcomprising one or more instructions that in response to being executedon a computing device cause the computing device to carry out a methodaccording to any one of embodiments 1 to 36.

Unless otherwise indicated, all numbers expressing quantities,properties, measurements, and so forth, used in the specification andclaims are to be understood as being modified in all instances by theterm “about.” The recitation of numerical ranges by endpoints includesall numbers subsumed within that range, including the endpoints (e.g. 1to 5 includes 1, 2.78, 7π, 3.33, 4, and 5).

As used in this specification and the appended claims, the singularforms “a”, “an”, and “the” include plural referents unless the contentclearly dictates otherwise. Furthermore, as used in this specificationand the appended claims, the term “or” is generally employed in itssense including “and/or” unless the content clearly dictates otherwise.As used herein, the term “coupled” includes direct and indirectconnections. Moreover, where first and second devices are coupled,intervening devices including active devices may be located therebetween.

The description of the various embodiments provided above isillustrative in nature and is not intended to limit this disclosure, itsapplication, or uses. Thus, different variations beyond those describedherein are intended to be within the scope of embodiments. Suchvariations are not to be regarded as a departure from the intended scopeof this disclosure. As such, the breadth and scope of the presentdisclosure should not be limited by the above-described exemplaryembodiments, but should be defined only in accordance with the followingclaims and equivalents thereof.

What is claimed is:
 1. A method to provide an interpolated position ofan incremental encoder, the method comprising: receiving a first signalfrom the incremental encoder; producing a coarse position of theincremental encoder and a lookup address based on the first signal;retrieving a lookup value representing an arcsine or an arccosine of avalue of the lookup address from a lookup table; calculating a fineposition of the incremental encoder using the lookup value; andproviding the interpolated position of the incremental encoder based onboth the coarse position and the fine position.
 2. The method of claim1, further comprising: receiving a second signal from the incrementalencoder, the first signal and the second signal having a quadraturerelationship; and producing the coarse position of the incrementalencoder using the quadrature relationship between the first signal andthe second signal.
 3. The method of claim 1, further comprising:establishing a first zero-crossing value for the first signal; obtaininga digital value of the first signal at a first time; ascertaining aquadrant of the first signal at the first time; computing a lookupaddress based on a difference between the digital value and the firstzero-crossing value; using the lookup address to retrieve the lookupvalue from the lookup table; and calculating the fine position based onthe quadrant and the lookup value.
 4. The method of claim 3, thecomputing the lookup address comprising: computing the lookup address bysubtracting the first zero-crossing value from the digital value inresponse to the ascertaining that the quadrant of the first signal atthe first time is in a first half of a cycle of the first signal; andcomputing the lookup address by subtracting the digital value from thefirst zero-crossing value in response to the ascertaining that thequadrant of the first signal at the first time is in a second half ofthe cycle of the first signal.
 5. The method of claim 3, the calculatingthe fine position comprising subtracting the lookup value from an offsetvalue in response to the ascertaining that the quadrant of the firstsignal at the first time is Q1 or Q3.
 6. The method of claim 3, furthercomprising: finding a local maximum of the first signal; finding a localminimum of the first signal; computing an average of the local maximumand the local minimum; and establishing the first zero-crossing valuebased on the average.
 7. The method of claim 3, the method furthercomprising: receiving a second signal from the incremental encoder, thefirst signal and the second signal having a quadrature relationship;providing a first indication to a quadrature-tracking state machinebased on the first signal crossing the first zero-crossing value inpositive direction; providing a second indication to thequadrature-tracking state machine based on the second signal crossing asecond zero-crossing value in a negative direction; providing a thirdindication to the quadrature-tracking state machine based on the firstsignal crossing a third zero-crossing value in negative direction;providing a fourth indication to the quadrature-tracking state machinebased on the second signal crossing a fourth zero-crossing value in apositive direction; updating the coarse position based on an output ofthe quadrature-tracking state machine; and ascertaining the quadrant ofthe first signal at the first time based on a state of thequadrature-tracking state machine at the first time.
 8. The method ofclaim 7, further comprising: finding a first local extreme of the firstsignal at a second time; setting the second zero-crossing value based ona value of the second signal at the second time; finding a second localextreme of the first signal at a third time; and setting the fourthzero-crossing value based on a value of the second signal at the thirdtime.
 9. The method of claim 3, further comprising: generating a scalefactor; and using the scale factor in the computing of the lookupaddress.
 10. The method of claim 9, further comprising determining thescale factor iteratively based on one or more captured local extrema ofthe first signal and a maximum value of the lookup address.
 11. Themethod of claim 9, further comprising multiplying the scale factor bythe difference between the digital value and the first zero-crossingvalue to compute the lookup address.
 12. An article of manufacturecomprising a non-transitory storage medium having instructions storedthereon that, if executed, result in: receiving a first signal from anincremental encoder; producing a coarse position of the incrementalencoder and a lookup address based on the first signal; retrieving alookup value representing an arcsine or an arccosine of a value of thelookup address from a lookup table; calculating a fine position of theincremental encoder using the lookup value; and providing aninterpolated position of the incremental encoder based on both thecoarse position and the fine position.
 13. The article of manufacture ofclaim 12, wherein the instructions, if executed, further result in:establishing a first zero-crossing value for the first signal; obtaininga digital value of the first signal at a first time; ascertaining aquadrant of the first signal at the first time; computing a lookupaddress based on a difference between the digital value and the firstzero-crossing value; using the lookup address to retrieve the lookupvalue from the lookup table; and calculating the fine position based onthe quadrant and the lookup value.
 14. The article of manufacture ofclaim 13, wherein the instructions, if executed, further result in:finding a local maximum of the first signal; finding a local minimum ofthe first signal; computing an average of the local maximum and thelocal minimum; and establishing the first zero-crossing value based onthe average.
 15. The article of manufacture of claim 13, wherein theinstructions, if executed, further result in: generating a scale factor;and using the scale factor in the computing of the lookup address. 16.An apparatus to provide an interpolated position of an incrementalencoder, the apparatus comprising: at least one input configured toreceive first information related to a first signal and secondinformation related to a second signal; a quadrature state machinecoupled to the at least one input and configured to track a quadraturerelationship of the first signal and the second signal, the quadraturestate machine providing a quadrant output and counter control lines; acoarse position counter coupled to the counter control lines andconfigured to increment and decrement under control of the quadraturestate machine; address calculation circuitry, coupled to the at leastone input and the quadrant output of the quadrature state machine, andconfigured to generate a lookup address output; a memory having anaddress input coupled to the lookup address output and storing arcsineor arccosine values of corresponding lookup addresses; and circuitry togenerate the interpolated position of the incremental encoder based onboth an output of the coarse position counter and an output of thememory.
 17. The apparatus of claim 16, further comprising: circuitry togenerate an offset value at an offset output; and a subtraction circuitcoupled to the output of the memory and the offset output; wherein theinterpolated position of the incremental encoder is based on both theoutput of the coarse position counter and an output of the subtractioncircuit.
 18. The apparatus of claim 16, further comprising: circuitrycoupled to the at least one input and configured to provide the firstinformation on a first output; circuitry coupled to the first output andconfigured to provide a zero-crossing value for the first information ona zero-crossing output; and a subtraction circuit coupled to the firstoutput and the zero-crossing output, an output of the subtractioncircuit coupled to the lookup address output.
 19. The apparatus of claim16, further comprising: circuitry coupled to the at least one input andconfigured to provide the first information on a first output; circuitrycoupled to the first output and configured to capture a local maximumand a local minimum of the first information and provide a local maximumoutput and a local minimum output; an adder coupled to the local maximumoutput and the local minimum output; a subtraction circuit coupled tothe first output and an output of the adder; and a multiplier coupled toan output of the subtraction circuit and a scaler output, an output ofthe multiplier coupled to the memory as the lookup address output. 20.The apparatus of claim 19, further comprising a scaler calculation statemachine configured to: iteratively determine a scale factor based on oneor more captured local extrema of the first information and a maximumvalue of the lookup address for the lookup table; and provide the scalefactor on the scaler output.